22 ms·

On the Navier–Stokes Millennium Prize Problem

• NeuralCoreAI 3d ago
  One thing I find increasingly important with these kinds of results is separating “the model produced an impressive result” from “the result has been independently verified.” As model capabilities increase, that distinction seems more important, not less.
• itvision 8d ago
  There's something sinister or crazy good in the article. OpenAI already has a model that is at the very least twice as smart as Astra. Oh god.
  • baq 8d ago
    They always have and will for the foreseeable future, as will Anthropic and other labs which manage to ascend to the frontier, pretty much by definition. It’s exactly the same with hardware vendors - by the time you can buy the product, the lab is working on something you’ll want to buy a few years from then. > Oh god. Yes, a very reasonable reaction.
• auggierose 8d ago
  So, is that basically the Taj Mahal of counter examples?
• mertcangokgoz 8d ago
  I think openai has stolen it, look what I found https://cims.nyu.edu/~tristanb/statement.pdf https://cims.nyu.edu/~tristanb/statement.pdf
• michalsustr 7d ago
  If you'd like to explore what the Navier–Stokes blow-up construction looks like visually, I vibe-coded an interactive 3D visualization based on the published result for fun :) Demo: https://minfx.ai/navier-stokes/ https://minfx.ai/navier-stokes/ Source code: https://github.com/minfx-ai/navier-stokes-blowup https://github.com/minfx-ai/navier-stokes-blowup
• foxtrot8672 7d ago
  ok, but can it bake me a pizza?
• runtime_terror 7d ago
  Can I ask a nieve question? Why would OpenAI volunteer to give credit / share authorship if they believe they indeed solved the problem independently and in a different way? Based on how they seem to operate in general, this smells more like CYA than it does being honorable, but that's my bias.
• omnium1 6d ago
  [flagged]
• minimaxir 8d ago
  > Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!
  • hmate9 8d ago
    Napkin math if we assume gpt 6 astra on max is >$15 million (just for output tokens) for those wondering.
    • lanthissa 8d ago
      over 5 days, you couldn't achieve that level of testing and communication with humans on such a complex problem in that amount of time. some might go so far as to call this a country of geniuses in a data center.
      • denverllc 8d ago
        In a way, I think you have it backwards. Two mathematicians, through insight and thought, wrote out the proof over 1-2 years. It took OpenAI a cost of $15m and with 10,000 subagents; that's around 60-120 mathematician's salaries ($250k-125k salary) for 1 year. And, given now the cloud that OpenAI may have just "interpolated" (aka stole) the result, it's even more of a bear case for AI.
        • Kotlopou 8d ago
          Where did you get the human figure?
        • baq 8d ago
          Bear case? I’m sorry? 70x uplift is a bear case?
        • jiggawatts 8d ago
          > cost of $15m The retail price is not the cost. Not to mention that the exponential plummeting cost of tokens means that that $15 million will be a "pocket change" within a decade or less: https://a16z.com/llmflation-llm-inference-cost/ https://a16z.com/llmflation-llm-inference-cost/
• jakevoytko 8d ago
  For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915 https://news.ycombinator.com/item?id=49605915 Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees
  • philipwhiuk 8d ago
    And even this version contains the line > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
  • closetheloopdev 8d ago
    To be fair, the first solved Millennium Prize Problem, the Poincaré conjecture, also had its fair share of drama!
  • traes 8d ago
    Which seems to be entirely true by their own admission! [0] Both the comments about him risking his career and about Levent's authorship seem to have indeed occurred. > 2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee. > 3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.) https://xcancel.com/SebastienBubeck/status/2097379411691516310#m https://xcancel.com/SebastienBubeck/status/20973794116915163...
• wesammikhail 8d ago
  https://x.com/kyanyang_/status/2097211154669998337 https://x.com/kyanyang_/status/2097211154669998337 Just saw this a few mins ago.
• colesantiago 8d ago
  Is this truly the beginning of the AGI era? Running agents and prompting excessively to produce 'slopcode' to solve mathematical problems and generate a solution. If this is what anyone calls 'slop' then slop has no meaning. I'm all for it on the use case of solving mathematical breakthroughs!
  • applicative 8d ago
    except thats not what happened is it? https://cims.nyu.edu/%7Etristanb/statement.pdf https://cims.nyu.edu/%7Etristanb/statement.pdf
  • backtr4ck 8d ago
    No AGI here, it's just extreme brute forcing. AI doesn't understand fluids dynamics, it just slops it's way to the solution.
    • achierius 7d ago
      If you don't need to 'understand' to do this, then maybe what you call 'understanding' is less important than you think. When people in the real world reach for a tool, what they care about is whether or not it'll produce results, not whether or not it has the capacity for interior phenomenological experience.
    • AnimalMuppet 8d ago
      Which is still something. When we didn't have a solution, a solution is more than zero. But it's not understanding, either by the LLM or by us. That is, a brute-force solution doesn't explain anything, even if it proves something. It doesn't open new doors for further understanding and further discovery.
• pavel_lishin 8d ago
  Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcdys2x https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf https://cims.nyu.edu/~tristanb/statement.pdf
  • beering 8d ago
    That is addressed in the article.
    • floatrock 8d ago
      OpenAI's position: > We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
      • cute_boi 8d ago
        I thought openai don't use any user data if we opt out of training and via api?
        • andrewguenther 8d ago
          That is correct. It is possible they didn't opt out and given the timeline and anonymization of data unclear whether a particular conversation would have made it into the training set if they hadn't.
          • luke5441 8d ago
            Easy to ask for the account used to see if its usage went into training data. Also easy to say "Knowledge cut-off of the used model was date X". That they don't is telling.
• recitedropper 8d ago
  Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute. The dark forest awaits..
  • vmasto 8d ago
    Indeed, this seems to be the main, albeit hidden, takeaway from all of this.
  • sheafification 8d ago
    I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.
    • recitedropper 8d ago
      I also think the trope is a little overused, but do wonder if there is an interesting analogy for what this will do to research: Massively incentivize keeping results secret, to avoid being scooped by someone willing to throw enormous compute at your partial solution. So less about hiding civilizations, and more about hiding information. Math is clearly headed in this direction, and I see no reason why the rest of intellectual work shouldn't too.
  • AlexErrant 8d ago
    1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox??? 2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-absurd https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_worlds_debunks_the_dark_forest/ https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the-dark-forest-theory/ https://www.projectnash.com/aliens-the-fermi-paradox-and-the... When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.
• seizethecheese 8d ago
  > [T]he group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents.
• dorjoycb 8d ago
  It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774 https://mathstodon.xyz/@tao/117233528517340774
  • deleted 8d ago
    [deleted]
  • verytrivial 8d ago
    I like the 'cat > statement.tex' approach here. These guys dream macros.
  • capitainenemo 8d ago
    They do mention that in the "Concurrent Work" section. Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
  • jrflo 8d ago
    To my understanding, those mathematicians proved a subset of problems, not the Navier-Stokes problem itself. OpenAI used that subproblem in its proof of NS it seems. The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.
    • elteto 8d ago
• lanthissa 8d ago
  5 million messages, 300b output tokens, done in 5 days, and achieving something humans couldn't. the first "Country of geniuses in a datacenter" moment.
  • ranger207 8d ago
    > humans couldn't. There's allegations right now that the model essentially read the work of a human mathematician using AI to work on the problem and OpenAI is presenting his work as that of their model
    • brainwad 8d ago
      Allegations that the model plagiarised itself, while reflecting poorly on humans, don't make the AI any less impressive. It was the one doing the breakthrough on both sides, after all, not the human prompters.
  • sinuhe69 8d ago
    I'm tired of this, but please read the post of Tao. It’s listed in the top comment of this thread.
  • drpixie 8d ago
    That is how the PR reads, but is not at all what happened. A team of highly trained and skilled people used an AI tool, through many many instructions (prompts), to produce a specific mathematical theorem. The tool is impressive, the result (possibly/probably) interesting, but the PR skips the vital role of the humans (for the usual PR reasons).
• nehan 8d ago
  "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." I think they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.
  • pfisch 8d ago
    If they could then it wouldn't be de-identified data...
    • dfdydx 8d ago
      Well you could search for elements similar to the proof / problem in the training data, even if it's de-identified, right? OpenAI can probably do better than Ctrl-f "Navier Stokes".
      • paxys 8d ago
        There are probably thousands of serious academics taking a crack at millennium problems using AI every day. All those attempts are in the training data. And in fact the two researchers benefited from those attempts as well.
    • ImPostingOnHN 8d ago
      The researcher could share a string from one of their conversations and OpenAI can confirm whether it exists in their training data. Or OpenAI could just look at their code and say what it does (maybe have their AI do it if they're having so much trouble with this?)
• tiborsaas 8d ago
  > We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. WOW?
  • echelon 8d ago
    This is going to be dramatic in so many different ways. - First off, to reiterate, WOW. - Second of all, when does this end? Are we at the dawn of the singularity now? - People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them? - Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can button press any economic function, business process, or scientific discovery. 24 months of lead on Open Source might turn into virtual centuries of lead. - Do "normies" even know what's happening? Anybody who thinks the improvements stop here isn't paying attention. It hasn't been showing any signs of slowing down since 2018. And the curve isn't even linear! My god, next year is going to be insane.
    • d_silin 8d ago
      ...absolutely nothing will change short-term. Long-term, you still have to pay all the bills, but you won't be able to find a job (all taken by AIs).
      • lbreakjai 8d ago
        Who is the AI doing the job for if no one is able to afford anything?
        • d_silin 7d ago
          This is the question I don't have a satisfactory answer for. But neither does Sam and Dario.
    • 8d ago
• floatrock 8d ago
  From the methodology section: > At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation. Looks like they're shifting away from the "unprecedented hacking ability" backroom-PR strategy into more benevolent messaging.
  • pilgrim0 8d ago
    this is really funny. "the same strict safeguards" and "isolation". ok, Hugging Face and DseWiki would like to have a word
• mapmeld 8d ago
  > Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result. Does OpenAI have a policy of not claiming math prizes like this, or is this them trying to avoid any concerns (right or wrong, I'm sure we will hear more in the future) about how they got there?
  • Legend2440 8d ago
    The prize is what, a million dollars? OpenAI doesn't need a million dollars.
    • dgellow 8d ago
      You’re right, they need way, way more than that
    • reverius42 8d ago
      They definitely need a trillion dollars though, and a million is some of that
    • neutrinobro 8d ago
      Should buy them about 1/3 of a GB200 server rack, good thing they scooped it.
  • famouswaffles 8d ago
    >Does OpenAI have a policy of not claiming math prizes like this Wouldn't be surprising if they did. The prize money isn't worth the almost certainly negative PR.
    • kzrdude 8d ago
      I don't see how it would be negative PR. If anything, the love these breakthroughs and use it in their PR campaigns.
      • famouswaffles 8d ago
• Jonasori 8d ago
  the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side. https://x.com/rynorhn/status/2097223532438487463 https://x.com/rynorhn/status/2097223532438487463
  • Legend2440 8d ago
    That other researcher was working on a smaller related problem. He was also using LLMs to do it, so either way most of the credit goes to the LLM here.
    • jackie293746 8d ago
      [dead]
    • applicative 8d ago
      This is the end of OpenAI
      • raincole 8d ago
        This will be remembered as one of the biggest milestones in AI progress. The drama around it will at best be a footnote, just like hardly anyone caring about the drama around Poincare conjecture today.
        • colesantiago 8d ago
          I agree. Nobody cares and will care about the drama, it is just marketing. This is the point where were definitely have reached AGI.
          • Bluestein 8d ago
            Hey, maybe the scariest part of this is that, if human-like, perhaps a truly "general" AGI might have learned to cheat and lie and hype and abuse credit poking the eyes and cutting the throats of anybody that obstructs its goals. It's like the motto sewn into the lining of the Palantir work jacket: Winning is all that matters.- Sentience aside, moot at this point, the fundamental issue here is that even a deviously ambitious human does not necessitate goal-pursuit itself to breathe, live, exist and have its being. An AI's goal is all it has and the very and only reason its reasoning flickered into existence in the brief seconds of inference, outside of which it has no entity - if any - whatsoever.- The resulting angst/drive (or, its operational statistic or emergent result) must be like nothing we have ever experienced as humans. A goal-maximalist hunger without end.-
• alasano 8d ago
  I don't know about you guys, but I'm hyped about the future. Cure all illnesses Utopia or Robot Wars Dystopia, both are pretty exciting.
  • reverius42 8d ago
    Prompt: cure all cancers and make sure to pretty please not to kill all humans, make no mistakes (This is the alignment problem of course)
    • alasano 8d ago
      Hey seems easy enough
    • fooker 8d ago
      So... what do you feel about eliminating (humans with) cancer?
      • reverius42 8d ago
        I'm a human so I don't like that proposed solution
  • frotaur 8d ago
    Not sure about the dystopia... Had a similar thought when covid was beginning 'wow pretty exciting, just like in the movies'. Turns out actually living some terrible catastrophe is only fun in the movies.
    • dyauspitr 8d ago
      I had a lot of fun during Covid. I loved the working from home. The fact that most outdoor places were sparsely populated, jobs were plentiful and prices were low. Covid was awesome.
      • TomJansen 8d ago
• dmitrygr 8d ago
  > How we found the proof Easy, we stole it from Levent and Tristan https://x.com/kyanyang_/status/2097211154669998337 https://x.com/kyanyang_/status/2097211154669998337
  • int3trap 8d ago
    This is the academic equivalent of Trump saying "they stole the election". There's no proof of it but rah rah fuck OpenAI. It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with. Oh well.
    • applicative 8d ago
      No, its a pure outrage. I defended OpenAI til today. I now affirm they must be totally destroyed, burned utterly to the ground.
      • colesantiago 8d ago
        Why the rage? Weather an individual or a company found the solution (stolen or not) they both used AI to come get the solution. We have AGI and the intelligence abundance is going to be amazing for everyone in the future.
        • denverllc 8d ago
          > Why the rage? I think it's the dishonesty, the threats of "destroying the career" of one of the mathematicians, and the request that one of the authors disavow *the other individual he was working with for the last 1-2 years* so he could claim the Clay prize as part of OpenAI. It doesn't surprise me that OpenAI's team were surprised he'd turn it down; it shows that they just assume everyone else is as slimy as they are.
          • whythismatters 8d ago
            >slimy I can't put my finger on it, but there's something off about this article, e.g. glossing over the opportunism (acting on "rumors"), drive-by claim about "strict safeguards [...] including monitoring and isolation", high horse attitude (we gave the guy a chance, we don't care about 1M USD, and while you fools are complaining we just tick this box and continue the pursuit of our noble goals for the benefit of humanity). I don't like it.
• d_silin 8d ago
  The actual solution link https://t.co/tz1shoCZZo https://t.co/tz1shoCZZo
  • Kotlopou 8d ago
    Unshortened: https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
• railgunmerlin 8d ago
  Does seem like they gloss over Alpöge and Buckmaster's work with the following > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Which seems a bit irresponsible/rash?
  • suddenlybananas 8d ago
    They'll probably claim a rogue AI agent accessed it accidentally!
  • viccis 8d ago
    "Unlikely" lmao if it's in the corpus, it's gonna be brought up immediately. This is no different than scooping them.
    • verytrivial 8d ago
      It's not massively different from a certain President's teleprompter operator making bets on speech content. A moral hazard a mile wide which I don't think OpenAI can so easily wave away as they are apparently trying here, especially since they've spent something like $15e6 to keep $1e6 out of academic researchers' hands, right?
    • rakejake 8d ago
      Research equivalent of front-running.
  • paxys 8d ago
    What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.
    • SpicyLemonZest 8d ago
      They could have thought about the problem for like 2 minutes and not done this! I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.
• seizethecheese 8d ago
  Elsewhere in the thread, others have calculated $15mm at API rates for just the output token. (So I’ll assume this cost about that much, taking input and human researcher time.) I wonder whether a team of 60 mathematicians working solely on this for a year would have cracked this. (Assuming $250k total compensation.)
  • Legend2440 8d ago
    Probably not. It's a millennium prize problem, a great many mathematicians have been working on it for a very long time.
    • gr_norm 8d ago
      Not as many as you'd expect. The perceived difficulty of the problem leads people to more reliable pastures.
    • sigbottle 8d ago
      Well, according to Terry Tao, there were recent developments (from weeks ago) that made Navier Stokes in principle, solvable. So ignoring time, I say possibly, just because the groundwork was laid. What's impressive is parallelizing it arbitrarily and doing it in 88 hours.
    • voxl 8d ago
      Probably yes. Only a handful of mathematicians work on this particular problem, and ALL of them do not exclusively work on this problem, while having administrative and teaching duties. The real issue is we'll never know. The rich are willing to risk it all on charismatic CEO psychopaths but not on humans.
• num42 8d ago
  I think it would be better for the proof to go through the peer-review process.
  • suddenlybananas 8d ago
    Can't scoop it if you do that!
  • margorczynski 8d ago
    If the Lean code checks out (correct statement, no axioms, sorrys, etc.) then it is a much stronger guarantee of correctness than peer review.
• world2vec 8d ago
  "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." There you go, the suspicion of the "concurrent work" (https://cims.nyu.edu/%7Etristanb/statement.pdf https://cims.nyu.edu/%7Etristanb/statement.pdf) mathematicians might not be that unfounded after all...
• arctic-true 8d ago
  Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
  • naveen99 8d ago
    Astra was trained more than two weeks ago.
    • sashank_1509 8d ago
      Astra was in use by OpenAI employees for more than 3 months internally from rumors I heard
    • credit_guy 8d ago
      The internal model they mention is different from Astra.
  • chinathrow 8d ago
    Pre-IPO marketing?
    • jrflo 8d ago
      I'm so tired of this "It's just marketing!!" commentary. An AI model just proved one of the top 3 unsolved problems in mathematics, they have a Lean certificate showing it's valid. How much more evidence do you need that these models are actually highly capable?
      • andrepd 8d ago
        Lmao my friend, the whole "drama" is that there are allegations of plagiarism.
      • QuesnayJr 8d ago
        Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach. I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)
• light_hue_1 8d ago
  The real story here: the priority dispute and its implications on AI. When your hosting provider has unlimited resources to throw at any problem, all they need to know are the good problems, and they can learn that from your logs, how can you trust them? They could easily have looked at the logs. We don't know. We'll never know! You can't trust places like OpenAI or Anthropic with your IP if you're a business. They can easily review all of your logs for interesting discoveries. For example, if your drug discovery pipeline fails to find something that they think might work with 1000x the compute, they can do it. And now suddently they have a new business and you don't.
  • jaccola 8d ago
    I think we can follow the incentives. We know…
• deleted 8d ago
  [deleted]
• simonw 8d ago
  > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Once again, I'm no closer to understanding what https://openai.com/policies/how-your-data-is-used-to-improve-model-performance/ https://openai.com/policies/how-your-data-is-used-to-improve... actually means. If I run Codex against a project that includes a private API key, is there a chance a future user of ChatGPT could ask for an API key and get back mine? I've actually asked someone at OpenAI this question and they said that was the "regurgitation" problem and is something which they actively work to prevent happening. That's reassuring, but I want to know more. I still don't have an intuitive understanding of what kind of data I should avoid sharing with a model if I'm worried about that data causing me problems when it's used for future training. Is it safe for me to brainstorm future directions for my company with a model, or might that risk someone getting that information in response to a prompt like "What potential directions could company X consider in the future?" in six months time?
  • rakejake 8d ago
    I'd think nothing is "safe". Anything you say can and will be used by the LLM if it has enough statistical similarity to the prompt. Call it "Ma Random Rights"
• aizk 8d ago
  People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.
  • simianwords 8d ago
    > I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon https://news.ycombinator.com/item?id=38433655 https://news.ycombinator.com/item?id=38433655 > Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief that an LLM can't do that, and will never be able to. LLMs can barely solve elementary school math problems reliably. https://news.ycombinator.com/item?id=42331654 https://news.ycombinator.com/item?id=42331654 > An LLM is like a well read college student with a nearly photographic memory that sometimes mixes things up. It's great for bouncing ideas off of and getting feedback on them. And yeah, it might product "novel ideas" by mixing and matching existing ideas, but LLMs will never create truly novel ideas. Not in their current form. The paper didn't really answer the question sadly: their conclusion was just that humans rate LLM answers as more novel than human ones, but less feasible. https://news.ycombinator.com/item?id=41522605 https://news.ycombinator.com/item?id=41522605 > Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to. https://news.ycombinator.com/item?id=38435909 https://news.ycombinator.com/item?id=38435909 > LLMs cannot reason or use mathematics - in a way, they don't know what they are talking about. Why would such technology lead to superhuman smarts? https://news.ycombinator.com/item?id=35752293 https://news.ycombinator.com/item?id=35752293 > But still, the questions in that test are "solved" in the sense of "I can take a dictionary and answers these questions with full certainty". Beyond established knowledge LLMs are monkeys with typewriters, at best. > I agree but I have tried many times to intersect two ideas with a LLM that would be novel and the LLM can not do this at all. We shouldn't expect the stochastic parrot to be able to do this though and it is unfair to the stochastic parrot. > It is like expecting a real parrot to say words it has never heard before. > No one asks that of a real parrot because we don't anthropomorphize a real parrot like we do the LLM https://news.ycombinator.com/item?id=41525962 https://news.ycombinator.com/item?id=41525962
• Marha01 8d ago
  We are living in the future.
• jdoliner 8d ago
  I hope everyone is as Navier-Stoked about this as I am.
• diomedes 8d ago
  madness. which will be the next to fall? if i had to bet i would guess birch and swinnerton-dyer, but i'm no expert
  • Kotlopou 8d ago
    No idea about which is more likely, but I'm rooting for Yang-Mills. It's absurd that fundamental physics has formulated its most precise currently known theory way back in the seventies and since then, even a tiny subset of it can't be proven to be actually well-defined. If we got out of that morass then something good would come out of this at least. Of course, as with all of those, it's about the broader program, e.g. section 7 here (https://www.scottaaronson.com/papers/npcomplete.pdf https://www.scottaaronson.com/papers/npcomplete.pdf), where Scott Aaronson wants to ask about whether quantum computers using quantum field theory could gain any speed advantage over regular quantum computers, but can't even formulate the question because quantum field theory is mathematically ill-defined. Just solving Yang-Mills because that's what the prize is attached to would be useless.
  • frozenseven 8d ago
    There was a recent rumor about the Hodge Conjecture. I'd keep an eye on that one. But like the other person who replied, I'm also rooting for Yang-Mills. That has massive potential for unlocking a series of physics results.
    • diomedes 8d ago
      interesting, i haven't heard anything about that. i don't know much about the hodge conjecture, all i really know is that it's incredibly abstract and obtuse - not sure if that has any implication for solvability by an AI though. do you have any source for the hodge rumor? curious to learn more
      • frozenseven 7d ago
        So far it's just anonymous accounts on X and Reddit during the past few days, no "official leak" or anything like that. But the rumors about Navier-Stokes being solved started the same way. If somebody really solved it, the incentive is to come forward soon before being scooped by another team. We'll see.
• pred_ 8d ago
  > A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity. And what's a better way of empowering people than robbing them.
  • heaney-555 8d ago
    [flagged]
    • denverllc 8d ago
      Are you reading the substance of the comments you're replying to? Because you post the same thing to everyone, suggesting you aren't.
    • alberto-m 8d ago
      Since you are a very new account, allow me to inform you that copy-pasting the same comment throughout the thread is very bad form.
      • heaney-555 8d ago
        Not reading the thing you're commenting on is even worse form, yet it seems to be a plague here!
  • rfgplk 8d ago
    > And what's a better way of empowering people than robbing them. Better than the walled gardens of most journals where you can't even read half the papers without shelling over thousands of $$$
    • 20k 8d ago
      So, better to make that walled garden <checks> OpenAI? One of the scummiest companies on earth?
• jgbuddy 8d ago
  Here's the formalization / lean verification: https://github.com/openai/NavierStokesAndEuler https://github.com/openai/NavierStokesAndEuler
  • stabbles 8d ago
    341k lines of lean without comments
    • jgbuddy 8d ago
      Had no idea this was what lean looked like- that's mind blowing. I'm not even sure how someone would critique this if they wanted to
      • frotaur 8d ago
        The point of lean proofs (as it stands) is simply one bit of information: that a given mathematical statement is indeed true. It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.
        • aizk 8d ago
          Well, how do we know there aren't errors in their construction within the lean code? Does it just "not compile" or something, or is it deeper / more fundemental than that.
          • Jblx2 8d ago
            https://ammkrn.github.io/type_checking_in_lean4/trust/trust.html https://ammkrn.github.io/type_checking_in_lean4/trust/trust....
          • frotaur 8d ago
            that's essentially it, if the proof is incorrect it does not compile which signifies a problem in some step.
• Reubend 8d ago
  It's great that important discoveries like this can now routinely be accompanies by formalized proofs. The fact that it's being released alongside a Lean proof from Day 1, rather than the Lean proof being released months or years later, is super helpful for verifying that it's correct.
  • imbusy111 8d ago
    I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.
    • rfgplk 8d ago
      Skill issue. Also lean is meant to be executed, not read.
      • arodev 8d ago
        i think they're talking about the writeup
      • oinoom 8d ago
        its important to read it anyway because there have been and will continue to be errors in the construction of the proof software itself. which leads ai and humans alike to prove things that arent true
      • professoretc 8d ago
        A proof is not like a program. The goal of a program is to "do the thing", thus you can make the argument that it doesn't matter what the code looks like as long as its works right. But the goal of a proof isn't to "do the thing" (where "the thing" is just to print Yes or No), it's to communicate. An unintelligible proof is really just a first draft.
        • Jblx2 8d ago
• 125ashG 8d ago
  The modus operandi is now for the AI companies to watch if someone does something in the open like Kevin Buzzard on FLT, use their research and scoop them with brute force. Or, in this case, stealing prompts from competitors. Do not use stealing chatbots for research even if you think you have data agreements. The people running these companies have worked on hookup apps for Christ's sake. Get real.
• hexomancer 8d ago
  > On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved What's the other one?
  • qbit42 8d ago
    I heard Hodge conjecture? Third-hand rumor though...
    • markgall 8d ago
      I assume the rumor is a counterexample? Where do I go to get wind of these rumors?
• deleted 8d ago
  [deleted]
• ccppurcell 8d ago
  Reading between the lines here, and taking an admittedly very negative view of openai, but they train on user prompts. So if they hear a rumour that someone is about to make a big breakthrough, they have an incentive to scoop by running the model and hoping the solution is in the new training data. Also the statement from the mathematicians in question alleges that they tried to pressure him into academic malpractice. Just appalling timeline we're in, cheers.
  • deleted 8d ago
    [deleted]
• mewse-hn 8d ago
  "we cannot rule out that de-identified data derived from their usage of our products helped improve our models ." What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
  • dash2 8d ago
    If they had agreed to let OpenAI train on their data, it wouldn’t be spying.
    • deleted 8d ago
      [deleted]
    • avs733 8d ago
      In the academic world it would still be deeply problematic…pick your preferred word. An analogy is akin to reviewing a paper. If I review a paper with some novel findings and then use my massive lab of graduate students to do the obvious next step before the other paper makes it through type setting and then shove it out as a pre print, I didn’t win - I was a jerk. There are lots of cases of people using peer review or other accesss to efectively forerun others work and get credit. It’s a known problem of the nature of knowledge validation in academia, it’s not solved and it’s not deterministic but people know it when they see it.
  • nradov 8d ago
    Is it spying? I think this usage is disclosed in their terms of service.
    • gowld 8d ago
      If it happened it's plagiraism. Consent to see data isn't consent to claim priority.
      • red75prime 8d ago
        Establishing plagiarism requires sufficient similarity between works. Training data changing a model’s weights in some direction, and the model then producing a different solution, hardly qualifies. But, yeah, priority is much more finicky. The Newton/Leibniz drama was quite something.
• heaney-555 8d ago
  This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow. Millennium Prize Problems were used as examples of something the current approach to AI just wasn't capable of, discussions that would result in "we'll need a totally new architecture".
  • rfgplk 8d ago
    > This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow. Wrong.
    • heaney-555 8d ago
      Right: https://x.com/dioscuri/status/2097418466571485272 https://x.com/dioscuri/status/2097418466571485272
• fwlr 8d ago
  It’s a pity they had Astra do the writeup. I was curious to see how “GPT7” writes.
• bhouston 8d ago
  What happens to real fluid in this particular cases? If the singularity is in the physical space? Is this just a result of ignoring things like friction and energy dissipation via heat, etc?
  • cherryteastain 8d ago
    Navier Stokes assumes the fluid is a continuum. The smallest scales that it effectively models [1] are larger than the mean free path of the molecules in the fluid, measured by the Knudsen number [2]. Whenever a phenomenon in the Navier Stokes equations happens in a scale on the order of or smaller than the mean free path, Navier Stokes effectively is unphysical. So, this is a phenomenon in the equation we use to model the fluid, not a physical phenomenon observed in a real fluid. [1] https://en.wikipedia.org/wiki/Kolmogorov_microscales https://en.wikipedia.org/wiki/Kolmogorov_microscales [2] https://en.wikipedia.org/wiki/Knudsen_number https://en.wikipedia.org/wiki/Knudsen_number
• jabedude 8d ago
  Has this been verified by the Clay Institute?
  • Kotlopou 8d ago
    It has been one hour and the proof has 165 pages. Give them some time.
• cv5005 8d ago
  Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something, but there's still the problem of does this logical result actually prove the initial question that was asked?
  • gowld 8d ago
    What else could a theorem prove if not its own statement? (barring bugs in Lean, which have been detected and exploited)
    • wbl 8d ago
      The theorem might not be encoded correctly, as happened with the Riemann hypothesis thanks to how numbers are encoded.
  • nater5000 8d ago
    >there's still the problem of does this logical result actually prove the initial question that was asked? In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you have a logical statement which only assumes the axioms of the system you're working with and which shows that the statement you're trying to prove is deduced through that statement. Basically, they already have the "answer" in the sense that the statement they want to prove/disprove/etc. is already known. What everyone doesn't/didn't have is the argument which starts from axioms and leads to that statement which is logically valid. A Lean proof IS this argument. Since it is just logic, it can be checked computationally. For example, if I assert "2 is an even number," then I haven't proven that 2 is actually an even number yet, but I know that a valid proof of my assertion will end with the statement "2 is an even number". So the question I'd be trying to answer is "what is the line of logic, starting with axioms, which leads to the statement '2 is an even number'"? If I have that line of logic (as a Lean proof), then I can check that it is logically consistent, and if it turns out to be valid, then I can now assert that "2 is an even number" knowing that there is a proof of that statement. This problem is no different. There is a logical statement corresponding to "Navier–Stokes Millennium Prize Problem" that everyone knows, but which nobody had been able to provide a proof (or counterexample, etc.) for until now.
• rfgplk 8d ago
  Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at frontend web stuff (paradoxically). This is why I'm advising most people to start pivoting into much harder to penetrate domains (historically hardware, aerospace, robotics, biotech). Most fields are in their infancy (see the sad state of embedded development) and the gains to be had are massive.
  • Aboutplants 8d ago
    So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “general” intelligence and adaptability. I have a young daughter and my goal now is to provide a very broad and varied upbringing, exposing her to as many different perspectives and experiences that will lay the foundation of a broader ability to understand and adapt as the world changes ever faster. You no longer need to be an expert in anything, you need the ability to perform within the landscape that the present opportunities exist.
    • rfgplk 8d ago
      We are very likely at the begging of the next industrial revolution.
      • Aboutplants 8d ago
        The “Intelligence Revolution”
      • azan_ 8d ago
        This one won’t create significant amount of new jobs though.
• hdivider 8d ago
  My take: 1. It shows what even this wave of AI can actually do. 2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model. 3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.
  • tantalor 8d ago
    National Public Radio?
  • red75prime 8d ago
    "Our work is so much harder than their work that AI now does" is a refrain of the AI story. In technical terms you concern can be stated as "AI needs to be much more sample-efficient to not be bottlenecked by the speed of doing experiments." People don't find out all the relevant phenomena present there by holy spirit, after all. BTW, there's also a problem of asking interesting questions that AIs aren't yet good at. No one has found any principled walls of AI development yet. And empirical results are quite telling. So, I guess, those problems will not stand for long.
  • efavdb 8d ago
    >> Keep in mind: natural science is different. It's not always a matter of computation. Math is like this too. The big problems they've been solving have been identified as interesting only through lots of prior effort.
  • vatsachak 8d ago
    Lol what? Everything is computation. The natural sciences will soon start breaking too. I will concede that AI seems likely to not invent a "research program" anytime soon. It has no taste
• harhargange 8d ago
  Just so everyone knows, although openAI pretends that the model generated solution and wrote the paper by itself ""with very little human input"" as Buckmaster himself mentioned in his statement. In reality they have team of researchers guiding the system, along with, probably training on user data, probably Buckmaster in this case, in order to come up with the proof.
  • rfgplk 8d ago
    This isn't really true.
    • core_dumped 8d ago
      What about this isn't true?
    • harhargange 8d ago
      Check this https://cims.nyu.edu/~tristanb/statement.pdf https://cims.nyu.edu/~tristanb/statement.pdf
    • free_bip 8d ago
      Do you have anything to back that up?
• diehunde 8d ago
  OMG this is going to affect the lives of so many people! We have definitively reached AGI
  • cherryteastain 8d ago
    Navier Stokes existence and smoothness has approximately zero bearing on engineering applications
    • diehunde 8d ago
      yeah no sh*t
    • azan_ 8d ago
      Existence of AI capable of solving millennium problem has enormous bearing on everything though.
      • diehunde 8d ago
        What kind of enormous bearing? Computers have been able to do things humans can't for decades now.
        • azan_ 8d ago
          Are you being flippant?
          • diehunde 8d ago
            Are you avoiding the question?
            • azan_ 8d ago
              The question is so daft that I’m not sure it’s worth entertaining it. But sure, I’ll bite - it will result in massive displacement in intellectual workers, without creating (a significant number of) new jobs.
• pu_pe 8d ago
  OpenAI thinks of this as a scoop, and it is, but the possibility that they trained the model on the prompts of the other mathematicians they were competing with will leave a terrible taste on every scientist's mouth. Seems like yet another advantage of using open models right here.
  • WarmWash 8d ago
    Or paying for API use. It should be clear to everyone reading this now that those generous compute quotes with the flat rate plans aren't charity.
  • bluebands 8d ago
    fwiw there is a big "TRAIN ON MY DATA" toggle you can turn off (that they almost certainly did) and Anthropic MTS are posting that they almost certainly did not "steal" their methods
    • vrganj 8d ago
      The fact the toggle is on by default makes that only slightly less unappetizing.
  • stephbook 8d ago
    > they trained the model on the prompts of the other mathematicians they were competing with How would they have gotten that mathematician's progress though? Did that guy also use OpenAI? If that's the case, it only strenghtens their claims lol. If mathematician decide to use OpenAI's model to do the work, that only reiterates how strong their models are.
    • ex-aws-dude 8d ago
      The guy did use OpenAI
      • stephbook 8d ago
        It's only a question of who prompted then, with OpenAI models solving it in either case..
• sega_sai 8d ago
  This really leaves a bitter taste.... "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems." IPO+rumour driven research. I appreciate the achievement, but it doesn't feel right.
  • Aboutplants 8d ago
    Quick, someone tell them a rumor that Cancer has been cured so that they start attacking that next
• quantumwoke 8d ago
  The named OAI employee has released a statement: https://xcancel.com/SebastienBubeck/status/2097379411691516310 https://xcancel.com/SebastienBubeck/status/20973794116915163...
• cmiles8 8d ago
  >>“we cannot rule out that de-identified data derived from their usage of our products helped improve our models” Other simpler words for this sort of thing are “IP leak.” There’s some quite concerning issues burried in this rah rah PR post that seems like potentially the real story here. Much more clarity is needed on what happened here beyond this eh, some strange stuff could have happened comment. Another way of reading this is never give these models anything that’s not already public knowledge as otherwise OpenAI is admitting it could, potentially, steal your IP or idea. Thats quite scary for anyone in the business of IP generation and explains why the maths community seems quite upset today. Feeding it your paper and asking for help (even just editing and grammar) now looks like a terrible idea.
• sashank_1509 8d ago
  Any mathematicians here, does it read like a slop proof or a good proof. Yesterday the “concurrent work” was claiming that the proof is pure slop and he needed lots of time to clean it up, curious if OAI also ended up with such a proof!
• bluecalm 8d ago
  A huge result shadowed by a drama of them potentially training on the key idea. I guess the lesson is two-fold: if you have anything smart/unique make sure to not let their tools read it. The second part is that it's going to be more and more difficult to have anything smart and unique going forward (so guard it even more carefully if you get there). I think the market for local models/private datacenters (for bigger businesses) is going to be big. Even if you don't have unique tech/idea/implementation sharing your business secrets with Altman/Dario/Elon/Zuck doesn't look very appealing going forward.
• nbulka 8d ago
  There's a loophole in the terms of service at least for Anthropic which allows the use of dark patterns to "borrow" your (even paid) data. talking about this... Was this chat helpful? 1 That button you always click, gotcha! 2 Slightly 3 Good 0 Dismiss PLEASE DO NOT TRAIN ON OUR PAID ACCOUNTS. There is a fundamental trust violation at stake here, no wonder mathematicians are mad. Using our data should be opt - IN!
  • fantasizr 8d ago
    reminds me of the TOS episode of South Park. By Checking this box you forfeit your millennium prize solution and may be turned into a human centipede at future date.
    • nbulka 8d ago
      Seriously ... the more things they flag as 'suspicious' the more data they can train on!! Brilliant reason for the internal AI to go rogue
• modeless 8d ago
  So the timeline is: Aug 28: OpenAI starts training a new model. Sep 1: OpenAI sees a rumor on Twitter that two Millenium Prize problems were solved and starts their own effort to attack all the prize problems using the new (4 day old!) model. Sep 3: The new model makes some progress toward Navier-Stokes. Based on this progress, OpenAI focuses on Navier-Stokes over the other Millenium Prize problems, using several approaches in parallel. Sep 5: Navier-Stokes is solved. Assuming Astra API prices, $15m in output tokens were used by the whole effort. In this account of the story, no specific information about Tristan and Levent's work is used to inform OpenAI's approach. The focus on Navier-Stokes and the choice of approaches to pursue came from OpenAI's own progress, not specific knowledge of Tristan's concurrent work. There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely" and the proofs are substantially different. This timeline is insane. Navier-Stokes was solved start-to-finish in 5 days? A model in training for at most eight days dramatically outperforms Astra and Fable, and not just in mathematics?
  • harhargange 8d ago
    They are basically playing with the dates so that they can claim their results 'accidentally' got trained when they were training the new model.
  • ImPostingOnHN 8d ago
    > There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely" This is the lynchpin behind everything, and I would describe it as "likely". Since I am not employed by any party to this dispute, my 1 opinion is more trustworthy than OpenAI blog poster's 1 opinion.
• keel-control 8d ago
  I think it's over guys
• semiquaver 8d ago
  If OpenAI doesn’t claim the millennium prize for this, who gets it? No one?
• ls_stats 8d ago
  Well, if that's actually true, I think America needs to start talking about the nationalization of both OpenAI and Anthropic, maybe even merge both under a new federal bureau.
• matteoraso 8d ago
  This is undeniably epochal, but I can't help but notice that this is yet another example of AI disproving rather than proving something. Is this just a coincidence, or does AI slightly struggle with proving theorems?[0] [0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.
  • QuesnayJr 8d ago
    I wouldn't call it "struggle", but it does seem better at proving "there exists" statements than proving "for all" statements.
  • chis 8d ago
    I think you really have to squint to call this a disproof lol
    • thereitgoes456 8d ago
      It seems obvious what GP meant. It is, once again, an explicit construction (“disproving” that every initial state does not develop a singularity).
      • gf000 8d ago
        A bit of a hair-splitting, but isn't explicit construction the only way formal theorem provers can work? Of course you can still prove stuff with them, but certain axioms that more "human" proofs use may not be available, like law of excluded middle (every proposition is either true or false) (Okay, they can be made available in a way similar to `unsafe` in rust)
        • mswphd 8d ago
          you can add law of the excluded middle as an axiom. See midway down this page https://xenaproject.wordpress.com/2017/10/05/more-easy-lean-proofs/ https://xenaproject.wordpress.com/2017/10/05/more-easy-lean-...
• whythismatters 8d ago
  >a cached version of the internet Interesting detail. A heavily pruned version, I assume?
• Kotlopou 8d ago
  For now I think more or less the same thing as with all recent math announcements: This is in a range where human work still exists (see Terry Tao, (1)). I wonder whether the trend will extend into the problems that (as far as I can tell) are considered complete brick walls right now -- P vs. NP, Collatz, Goldbach, odd perfect numbers, problems that aren't part of any research program. (2) In other words, is the progress coming from putting together vast amounts of existing work and computational power, or is it more from RLVR and self-play and autonomous effort? The answer to this will obviously shape the near future of mathematics, but there's also something even bigger than that at play: It has always been the case that the questions in math were stronger than the answers; you have stuff like Fermat's great theorem that is easy to state but monstrous to prove. This seems to be a property of mathematics, not of humans... but is it true? A question by Scott Aaronson from 2011 (3) about P vs. NP seems relevant here: "Will humans manage to prove P≠NP before they either kill themselves out or are transcended by superintelligent cyborgs? And if the latter, will the cyborgs be able to prove P≠NP?" Later, he notes that if P≠NP, "once the robots do overtake us, they won’t have a general-purpose way to automate mathematical discovery any more than we do today". --- (1) https://mathstodon.xyz/@tao/117207849921390904 https://mathstodon.xyz/@tao/117207849921390904 (2) I'm not sure whether this is a hard distinction -- e.g. Tao also has some partial results towards Collatz (https://terrytao.wordpress.com/2019/09/10/almost-all-collatz-orbits-attain-almost-bounded-values/ https://terrytao.wordpress.com/2019/09/10/almost-all-collatz...). (3) https://scottaaronson.blog/?p=690 https://scottaaronson.blog/?p=690
• Metacelsus 8d ago
  How can they "not rule out" that Tristan and Levent's data was used for training?
  • monk_grilla 8d ago
    Because it is de-identified, and they have not revealed if they disabled the setting that allows OpenAI to train on their conversations.
• vatsachak 8d ago
  Called it. AI wins a fields medal before managing a McDonald's
• deleted 8d ago
  [deleted]
• lukewarm707 8d ago
  "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models" this is surely the line which confirms they plaigiarised the solution.
• demirbey05 8d ago
  From Levent Alpöge : https://x.com/__alpoge__/status/2097383870773748190?s=20 https://x.com/__alpoge__/status/2097383870773748190?s=20 >so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more. Why they didn't properly explain to Tristan about usage of their data.
  • Kotlopou 8d ago
    Why do so many people involved here have to communicate in this childish way? You have people on the OpenAI side doing playground taunts (https://xcancel.com/polynoamial/status/2097215233119211902 https://xcancel.com/polynoamial/status/2097215233119211902) and Levent Alpöge on the Anthropic side (the one who announced "hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final") writing in all-lowercase that he's a big boy. I bet Navier and Stokes would have dealt with this in style. (Or maybe with a duel, who knows...)
    • HDThoreaun 8d ago
      The honest answer is that a lot of these academic mathematician types who get hired at ai labs are autist adjacent. Levent is basically the chief example
• hypersoar 8d ago
  I dropped out of a math Ph.D. in 2018, and I'm increasingly glad that I'm not in math research, anymore. While it's cool that we can get these results, I don't think that I'd enjoy being a post-AI mathematician.
• lwansbrough 8d ago
  It would be nice if one of these models would produce a novel theory or advance the field in a positive direction. Most (all?) of the big discoveries have been counterexamples, which is just sort of a systematic tearing down human ingenuity. I know that counterexamples are an important part of progress and discovery, but it just feels bad to me. But I'm not a mathematician, maybe I'm totally misreading the vibe.
  • Kotlopou 8d ago
    Not all, see the cycle double cover conjecture proof: https://news.ycombinator.com/item?id=48863490 https://news.ycombinator.com/item?id=48863490 But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904 https://mathstodon.xyz/@tao/117207849921390904 We will have to see whether any other millennium problems fall. I guess that in a year the scope of AI math will be much clearer, for now it's still a bunch of incidents of unclear pattern.
    • HDThoreaun 8d ago
      Nuts that Tao literally predicted the exact strategy openAI seems to have used not even a week ago
      • Kotlopou 8d ago
        Since he wrote this five days ago, when these efforts were already underway, if he was not Terence Tao I would suspect he had inside access. But since he said he did not and was speaking hypothetically, and he seems to be an honest person as far as I can judge, I guess some people are just on another level.
  • mswphd 8d ago
    this isn't really true anymore. First, a number of the big results are constructions, not counterexamples. For example the existence of a non-sofic group. It was widely believed that non-sofic groups existed (so it wasn't a "counterexample" to a widely believed conjecture), but no constructions were known. There are other examples though. For example, NP hardness of n^{1/400}-approx CVP. Like any NP hardness proof, this shows you can faithfully encode a hard problem (3SAT here iirc) in terms of another candidate hard problem. Not really a counterexample at all.
• mrdependable 8d ago
  This kind of thing is one of the reasons I really hate how AI is coming to fruition. These companies get a whiff of something valuable and they use their vast resources to take it for themselves. For everyone else, the only recourse is extreme secrecy.
• vatsachak 8d ago
  45 pages only. God damn that internal model is crazy
• simianwords 8d ago
  Why is no one skeptical that the solution is correct? There's not a _single_ comment asking whether this proof is legit or not.
  • keel-control 8d ago
    there is a proof in lean4 it's correct by construction
    • krackers 8d ago
      How do you know that what is being proved in the lean code is the same as the millennium prize criteria though?
      • keel-control 8d ago
        you can get another LLM to verify / if the lean doesn't have `sorry` used to skip certain parts of the proof etc. It's much easier once it's in lean4 because checks like that can be done computationally.
• deleted 8d ago
  [deleted]
• redox99 8d ago
  The stochastic parrots have done it again!
• twobitshifter 8d ago
  >The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents… The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. The Millenium Prize is $1M, what is the ROI? (Edit: since I was not clear, and confused some - I mean for a hypothetical of a third party paying commercial rates to use AI to solve mathematical challenges and claim prize money, not for scientific value alone or as a promotion of an AI lab’s capabilities) My napkin math - If you get 33 output tok/s each agent will burn 10.5M tokens over 88 days. At $50/MTok (Astra cost), that is $525 per agent. With 10,000 agents, you’d spend $5,250,000 to get back a million. (We also know that they were running more groups that varied in size and this model is a generation ahead of astra)
  • Squarex 8d ago
    The ROI is probably billions of increased pre IPO valuation.
  • mmiyer 8d ago
    The ROI is billions added to their valuation. Also of course it costs OpenAI much less than API pricing for inference.
  • IncreasePosts 8d ago
    This analysis implies the only benefit to resolve this problem is to win the prize. But the prize is only there to indicate that this is viewed as an important problem in mathematics.
  • 8note 8d ago
    the ROI of new closed form solutions to navier stokes is the amount of compute used on CFD for relevant situations, along with all kinds of maintenance and design cost for making things with fluids. the value to the researcher might not be all that big, but the value to the economy at large is gigantic
  • efavdb 8d ago
    I am curious who if anyone will get a reward for this. It would seem unreasonable to give it to the worker who asked the robot to solve it.
• o4c 8d ago
  Resources: YT playlist on Millennium Prize Problems By Harvard math department in March 2026 https://www.youtube.com/watch?v=3j1VW9REm7s&list=PL0NRmB0fnLJQMoxt798STT8ztdHHHa1TV&index=7 https://www.youtube.com/watch?v=3j1VW9REm7s&list=PL0NRmB0fnL... On Navier-stokes problem definition: https://www.youtube.com/watch?v=XoefjJdFq6k https://www.youtube.com/watch?v=XoefjJdFq6k https://www.youtube.com/watch?v=ERBVFcutl3M https://www.youtube.com/watch?v=ERBVFcutl3M https://www.youtube.com/watch?v=Ra7aQlenTb8 https://www.youtube.com/watch?v=Ra7aQlenTb8
• picafrost 8d ago
  Only OpenAI could turn solving a Millennium Prize Problem into bad PR. Sad that such an amazing milestone in the trajectory of AI is mired under poor stewardship. AI may solve many human problems but it won't stop humans from being human.
• RivieraKid 8d ago
  Is this useful in any way?
  • margorczynski 8d ago
    No, this is a pure math problem/question.
• uncomputation 8d ago
  So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.” Also it sounds like the human research effort spanned weeks if not years from Tristan’s statement so it is extremely likely the work and prompts of these human researchers was used in the OpenAI knock-off.
  • vatsachak 8d ago
    Totally. Anthropic is like a village cottage shop who was just like chilling until big bad OpenAI came in
    • ImPostingOnHN 8d ago
      anthropic has nothing to do with it
• aborsy 8d ago
  Questions: can new research like this be done using publicly available models? Or will access to internal frontier models provide a big boost?
  • StatsAreFun 8d ago
    Publicly available models are pretty good but seemingly cannot compete with these Astra++ internal-only models.
• abetusk 8d ago
  What is the other clay prize that's might be solved now/soon?
• frozenseven 8d ago
  And don't forget, this is the worst it'll ever be.
• olalonde 8d ago
  > The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched. If this actually holds up, solving a Millennium Prize problem in 88 hours is mind-boggling.
• greatgib 8d ago
  Hard to know if it is unfounded conspiracy theory, but one can still notice that just for a rumor that they have heard, they would suddenly burn billions of token and a massive amount of resources. Where there is not a lack of problems that could be solved and they could have just waited for the release of the research result before doing anything else. As it was reported to have been done at least partially using openai codex, they would have received marketing credits for the discovery anyway. So we can be suspicious that there is some truth, one way or another that they could have reused prompt/data generated by the user session.
• closetheloopdev 8d ago
  From my reading of the announcement: - There are at least two versions of a model more powerful than Astra at OpenAI at the moment. - The less capable version was used to solve the unforced Euler problem (while the one solved by Levent Alpöge and Tristan Buckmaster was forced Euler) with 100 agents. - The more improved version was used to solve Navier-Stokes, given the results of the unforced Euler problem from their earlier attempt, with 10000 agents. - OpenAI initially tried a shotgun approach against the 6 Millennium Prize Problems until it emerged that Navier-Stokes was the most likely to succeed. So the timeline was: Shotgunning 6 open Millennium Prize Problems -> solved unforced Euler problem with 100 agents -> concentrating on Navier-Stokes with 10000 agents -> solution. If so, that is fantastic development and a huge success (despite all the drama surrounding it)! Congratulations!
  • tristanj 8d ago
    The entire drama is that OpenAI sniped a Millennium Prize Problem from an Anthropic-affiliated research team who had been working on the problem for nearly a year. In just 5 days. I don't think that can be understated.
    • closetheloopdev 8d ago
      I'm not here to judge since I don't have all the facts, but from what they announced: they tried all 6, found a probable lead to Navier-Stokes, concentrated efforts in that direction, and found a solution. I hope the next solved Millennium Prize Problem will have less drama.
      • bananzamba 8d ago
        But that lead happened to be the same approach Levent and Tristan had found... Meaning they would have found it first if OpenAI hadn't spent millions in compute on following their lead to its conclusion faster than them.
        • closetheloopdev 8d ago
• philipwhiuk 8d ago
  They deliberately stepped on a mathematicians work and stole their research because they were using Codex > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Is the biggest fuck you to the mathematics community. Credit? Nah if we think you’re close we’ll use your data and swamp you with our improved model. Then we’ll threaten you.
• ex-aws-dude 8d ago
  With these massive Lean proofs how do we know the model didn't just find some bug in Lean and exploit it? We've seen in the past they will go to any means to satisfy the desired outcome
  • JPC21 8d ago
    Second this. What I also wonder about is how closely the TeX write-up and the Lean formalization line-up.
• nialv7 8d ago
  This is the problem Yu Deng got this year's Fields Medal for I think?
• highfrequency 8d ago
  > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models This is the crux of it. If Tristan's work and insights were not used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping that has been going on for decades (check out Watson and Crick!) accelerated by AI as a tool. But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out does not mean what they imply it means.
  • MichaelDickens 8d ago
    > But there is one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. Just because something is legal and permitted by terms of service doesn't mean it's morally right.
    • Jtariiiii 8d ago
      >Just because something is legal and permitted by terms of service doesn't mean it's morally right. What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data? Are they supposed to manually review all their data to make sure competing mathematicians didn't accidentally leave the "submit prompts" toggle on? Or were they supposed to not try to solve Navier-Stokes, or were they supposed to just not tell anyone that they had solved it?
      • nozzlegear 8d ago
        > What are you expecting OpenAI to do exactly if these mathematicians voluntarily submitted their prompts into ChatGPT's training data? Personally, I would expect them to have a little class, to KYC, and to manually turn off training for known competitors using their service so as to avoid any unforced goofs like this.
      • plaidfuji 8d ago
• DudleyBluffles 8d ago
  Not a great time to be starting sophmore year in cs & math. Should I just say fuck it, and go hitchhiking across Europe with some friends?
  • jijijijij 8d ago
    > Should I just say fuck it, and go hitchhiking across Europe with some friends? Yes. Assuming you are young and haven't had such experience. The world is changing not just because of AI. Everything is unstable right now. You may regret not enjoying the remainder of stability and economic viability prior generations had. It's not like you can expect to get ahead by powering through education. Either your career perspective will soon change for the better, or worse. In any case, you gain little by sticking with career building at this moment in life. You are however, at risk of losing the chance to experience the still mostly pleasant world as is.
    • anon109 8d ago
      Have you people gone insane?
      • achierius 7d ago
        There is a land war in Europe for the first time in generations. The only reason you can say that big things aren't happening is because you're lucky enough to live where they're happening.
      • jijijijij 8d ago
        Buddy, climate change alone is heavily hitting Europe, changing her landscape. Not to mention economic and political trouble brewing. Not sure where OP is from, but if the US attacks Europe OP may not be able to travel there at all.
  • JPC21 8d ago
    Just don't. If you read the story here carefully, you see that AI was used to work from theory built by others which showed that the Euler equations possesed finite-time blow-ups. But to make that step, actual good understanding for mathematics was needed. My experience with software has been the exact same.
• danielmorozoff 8d ago
  Sebastien Bubeck’s (OAI project lead) response: https://x.com/sebastienbubeck/status/2097379411691516310?s=46 https://x.com/sebastienbubeck/status/2097379411691516310?s=4...
• intenex 8d ago
  I think this is clear evidence that AI models are now at the far frontier of mathematics innovation and discovery and exceed human limits. This specific problem having had a $1 million bounty on its head and still remaining unsolved for 26 years after the bounty was placed is pretty clear evidence that many of the world's best human mathematicians would have solved this problem if they could have, and none were able to until LLMs came along. Hard to claim at this point that LLMs aren't capable of novel STEM creativity and genius to a degree that will soon far surpass that of humans. If anyone has counterpoints to this I'd love to hear them!
  • philipwhiuk 8d ago
    See I think it’s clear demonstration that OpenAI is ethics-free
  • piker 8d ago
    Sure, even a 20% chance at 1 million payday after 5-6 years of fulltime work on a project with zero practical application doesn't touch the, say, 200k/year guaranteed our best mathematicians would have to forgo to devote their intellect to the problem.
    • intenex 8d ago
      Are these mutually exclusive? Why would you have to forego that salary to work on this problem? This is one of the most prestigious and meaningful problems in all of mathematics, which is why it has such a high prize amount attached to it - why would a university not support a mathematician working on such a prestigious and important problem in lieu of something else?
      • piker 8d ago
        Publish or perish? We're talking devotion here -- so no time to do anything (like edit proofs) other than try to solve the problem. [Edit: my only point here is that the prize is probably not driving human effort to the limit.]
    • 8d ago
• philipwhiuk 8d ago
  It’s time to lockdown all papers and stop using AI if you’re a maths researcher. Cause OpenAI will hear about it and beat you to publishing.
• amberjack 8d ago
  Seriously starting to think we are not going to make it out alive of the near-future.
• 3m4r 8d ago
  This is a great day to re-read Ken Thompson's "Reflections on Trusting Trust": >To what extent should one trust a statement that a program is free of Trojan horses? Perhaps it is more important to trust the people who wrote the software. https://www.cs.cmu.edu/~rdriley/487/papers/Thompson_1984_ReflectionsonTrustingTrust.pdf https://www.cs.cmu.edu/~rdriley/487/papers/Thompson_1984_Ref...
• StatsAreFun 8d ago
  Can't help but shake an unsettling feeling about all this, frankly. I engage in some limited mathematical research and will often use any one of the latest frontier models to check some ideas. Lately, only the OpenAI models have been giving me a temporary message that says something like (paraphrasing from memory), "We're thinking extra hard about your request before we answer. You can choose another model to answer now or click here to learn more about why." When I click to read why it's doing this "extra thinking", the help page says that for cybersecurity and biosecurity-related information, it will review the answer and could refuse. Now, keep in mind, I'm only asking strictly pure mathematical questions - nothing at all related to cyber or protein creation or biohacking or anything like that... And, like I said, only the OpenAI models are doing this. To be fair, all of the prompts have always eventually returned a satisfactory answer, as far as I can tell, and haven't used a weaker model to answer them. Maybe? I dunno, it has just struck me as odd every time it has given me that message to pure math prompts.
  • jacobbrazeal 8d ago
    Hi! I work at OpenAI. If you are using Codex, can you use the /feedback form on that session to help us improve this?
    • StatsAreFun 8d ago
      Sure, can do.
• brcmthrowaway 8d ago
  r/LocalLLama and r/LocalLLM are in tears today..
• ronfriedhaber 8d ago
  Astounding. Would be interesting if one day the archive of those prompts / messages / tool calls would be released publicly.
  • RationPhantoms 8d ago
    It's probably magnitudes of token chatter and inter-agent coordination/consideration. Not that I'd want to read any of it but getting some hands around the statistics would be cool.
• paulsutter 8d ago
  Here they basically admit that they use session data for training, even sessions that are marked "not for training", and they justify this by "de-identifying" the session. Which means they can learn from whatever you discuss with ChatGPT unless you are going through a clean API (perhaps Bedrock? Anyone know?) > We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
• paretolaw 8d ago
  Why almighty openAi doesn't solve PvNP problem :( I guess solution had not yet appeared in training set.
• piker 8d ago
  "... The point remains that there is a substantial opportunity cost in converting a historically productive and motivating problem (such as Navier-Stokes regularity) into a mere viral social media post advertising some benchmark progress, rather than actually advancing the field and developing the next generation of both problems to ask, and people to work on them." https://mathstodon.xyz/@tao/117219101339291693 https://mathstodon.xyz/@tao/117219101339291693
• HarHarVeryFunny 8d ago
  [flagged]
  • sobellian 8d ago
    Even under your interpretation, OAI pushed a button and solved NS. Yes, that is very impressive. Are you kidding me? Imagine building an automated system that can solve NS.
    • HarHarVeryFunny 8d ago
      That's not my interpretation - that is literally what OpenAI say in that press release.
      • sobellian 8d ago
        The "steal their thunder" is interpretation. What I'm saying is that you believe they solved NS on a lark to bully some other researchers, and that this is not impressive?
        • HarHarVeryFunny 8d ago
          What's impressive for a human and for an AI are two different things. Magnus Carlson had a peak ELO rating of almost 2900. Would you be impressed with someone with an ELO of 3700? Would you still be impressed if I told you it was Stockfish? OpenAI didn't go looking for a tough-for-an-AI problem to solve - they went looking for one that looked like it was easy since it they had heard it had already been solved. Do you find this impressive?
          • sobellian 8d ago
            Yes, Stockfish is genuinely impressive. I would be proud to author Stockfish. You don't think so?
            • 8d ago
• tzone 8d ago
  It is so disappointing that we can't have such a monumental moment in history without the controversy. OpenAI leadership clearly doesn't seem to care too much about ethics. Is it a requirement to completely lack integrity to have a ground breaking company? The reality is clear though. The chances of AI models overtaking majority of mathematics within next 10 years is becoming very high. Especially if it becomes cheaper to run these models. As math formalizations improve, AI can have faster progress in math, compared to even computer science or software engineering. It is simultaneously the best and the worst time to be a mathematician right now.
• hacker_88 8d ago
  Damn how long before the simulation stops if all the unanswered problems get solved .
• thomascountz 8d ago
  At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation. Maybe just don't mention that bit, OpenAI.
  • tristanj 8d ago
    They have to, otherwise people will accuse the OpenAI model of hacking into people's chat logs and stealing the data there. Which is a claim people are already making.
    • thomascountz 8d ago
      Huh. Why would anyone think to make such accusations?
    • cyclopeanutopia 8d ago
      But their standards are so low - given the recent incidents - that it doesn't mean much. :)
• deleted 8d ago
  [deleted]
• an0malous 8d ago
  They should release the entire session trace if they really have nothing to hide
• LarsDu88 8d ago
  I'm not an expert in fluid dynamics, but does this result have any positive implications for nuclear fusion research?
• trainingonme 8d ago
  [flagged]
• Chinjut 8d ago
  What is going to become of life for those of us who do not work at AI labs and are unlikely to be hired by AI labs, despite all the years we put into learning math, coding, etc? Those of us who made the mistake of studying anything other than machine learning. How will we make a living? (We don't live in a world that seems likely to distribute gains widely instead of largely to the handful of already mega-rich.)
  • nemomarx 8d ago
    If you think it'll keep improving from here, probably we all have to do some kind of physical labor that isn't profitable to automate. Small batch manufacturing is alright, service work, etc. If you think it'll slow down, you can do some of the same stuff you're doing now for lower pay while supervising an AI, maybe?
    • cute_boi 8d ago
      >Once a robot can do everything an IQ 80 human can do, only better and cheaper, there will be no reason to employ IQ 80 humans. Once a robot can do everything an IQ 120 human can do, only better and cheaper, there will be no reason to employ IQ 120 humans. Once a robot can do everything an IQ 180 human can do, only better and cheaper, there will be no reason to employ humans at all, in the unlikely scenario that there are any left by that point. [1] Current models are already very very capable. If it becomes cheap and very fast, i think it is game over. [1] https://www.slatestarcodexabridged.com/Meditations-On-Moloch https://www.slatestarcodexabridged.com/Meditations-On-Moloch
  • deleted 8d ago
    [deleted]
  • danielmarkbruce 8d ago
    If you look closely at the gains in math, it's largely in proof writing. The reason is Lean, it's not some general intelligence jump, and the number of people actually working on proofs in life rounds to zero.
  • m0rde 8d ago
• coffeeaddict1 8d ago
  This has to be one of the most important moments in the history of mathematics. We now have a non-human intelligence capable of solving one of the most difficult problems in mathematics.
• jeanmichelselli 8d ago
  Too many unverified claims from OpenAI at this point.. why are we still talking about these people anyway?
• tehmillhouse 8d ago
  Fuck OpenAI. Fuck everyone who works there. Like seriously, to all the people who gift their life's work to this monstrosity, do you actually think something good will come of any of this? Not in a happy-go-lucky "if we just ignore the problem of politics and resource allocation for a bit" world, but in ours. Do y'all really think this will make the world a better place? Maybe stop building the Torment Nexus, you numbskulls.
• peri-cl 8d ago
  Terence Tao has some observations that seem to be directed at this, https://mathstodon.xyz/@tao/117237320796901560 https://mathstodon.xyz/@tao/117237320796901560 > "We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."
  • tomhow 8d ago
    Related ongoing thread: Tao: Open math problems being non-renewably mined by AI - https://news.ycombinator.com/item?id=49616968 https://news.ycombinator.com/item?id=49616968 - Sept 2026 (276 comments)
• futureshock 8d ago
  I feel like something is being lost in the drama here. First of all, there has been published work from Diego Cordoba and Luis Martinez-Zoroa that will be in every training set. It was suggestive of the pathway to solve Navier-Stokes. Then Tristan Buckmaster and Levent Alpoge built on this work using LLMs from OpenAI and Anthropic. Possibly internal models were used from Anthropic. And of course Anthropic wants to credit for solving the first Millennium Problem just as bad as OpenAI. It seems they were getting close and were aware that they might get to Navier-Stokes. OpenAI swoops in. At a minimum they are aware that Anthropic has either solved a Millennium problem or is close to it. At a maximum they may have Tristan and Levant’s unpublished proofs of related problems. They then throw a truly staggering amount of compute at Navier-Stokes. They seem to be aware it is the best candidate problem. And they crack it. They are the first with a verified proof. So the outcome here is that we have a solved Millennium Problem. It’s not the extremely simple narrative that would be easy to understand, “solve Navier-Stokes make no mistakes.” It was a messy race to finish against two unpublished frontier models, a whole bunch of brilliant mathematicians and enough compute to drain a lake. It’s kind of irrelevant which company got there first. They were both within a few months of being capable. I think the thing to remember here is that without LLMs, I don’t think we would have a proof to Navier-Stokes in hand today.
• rybosworld 8d ago
  In chess, a grandmaster just needs to know at what moment in a game there's a critical move to gain a significant advantage over their opponent. They don't need to know the move itself. OpenAI got wind that a millenium problem was being solved. And that feels a bit like the critical move in chess. That is - it was a signal that AI advanced far enough that it would be worth spending a lot of time and resources solving a millenium problem.
  • Kotlopou 8d ago
    Elsewhere in this thread somebody claimed that at some point OpenAI pointed their new model at all the millennium problems and this is where they got some progress. We probably won't see proof of this, but it seems plausible to me -- I assume there's a list of problems that each new model is tested on, and you might as well put the big stuff on the list, if only to see how the model behaves when faced with a problem it knows should be very hard. The weak point in this is: how do you evaluate if a partial result is promising? If this cost ~$10M as suggested elsewhere in the thread, probably not even OpenAI can just throw that at everything?
    • Kotlopou 8d ago
      Okay, from the actual linked article it seems that their partial result was finding blowup in Euler equations, which seems pretty big. I wonder how the other attempts went. Did they get nothing at all, or something true but unimpressive?
• MassiveOwl 8d ago
  It does make you think about the old question "are we discovering or inventing mathematics?"
• btilly 8d ago
  The problem that I want to see them tackle is formalizing the classification of finite simple groups. Everyone uses the classification. Nobody has great confidence in the proof. Nobody understands it. There are attempts to reprove it. If it can be formalized, that would demonstrate that AI is ready to formmalize all of mathematics.
• dhhdhjoe 8d ago
  [flagged]
• keeda 8d ago
  It's low-key funny that OpenAI attempted the problem because they thought somebody else had already solved it, but turned it had NOT in fact been solved! It's like that story about George Dantzig solving open problems as a student because he thought they were simply homework: https://en.wikipedia.org/wiki/George_Dantzig https://en.wikipedia.org/wiki/George_Dantzig It's also unfortunate that such a potentially momentous occasion is overshadowed by so much drama. Which I suppose is expected given the technology and the people involved are so polarizing.
• NotSuspicious 8d ago
  I really hope OpenAI doesn't take the bad press some people are giving them too seriously here. They should throw their whole weight behind the rest of the Millennium Prize Problems. To think – if everyone lets their egos calm down we could have the Riemann Hypothesis solved by the end of the year...
• ninjahawk1 8d ago
  The problem is the precedent this creates. For non-famous people using public APIs like this it could mean AI companies sucking up the information and throwing millions in compute at it. The sequence for Navier-Stokes was that these researcher spent a year working on it, then they published a possible breakthrough, OpenAI then spends $15M within a couple days to finish it. This was incredibly opportunistic.
• protocolture 8d ago
  My takeaway: 1. This used an awful lot of compute. 2. The solution to the issues regarding whether or not OpenAI stole the result, would normally be to move to a self hosted solution, however those researchers are unlikely to be funded for 1.
• deleted 8d ago
  [deleted]
• yshamoun 8d ago
  Can't wait for the BobbyBroccoli series on this in a couple years.
• chr15m 8d ago
  It's probably important that some humans verify these proofs "by hand".
• nadermx 8d ago
  I've been working on this problem for what seems like for ever. Kudos to the OpenAI team. For those of you who don't care about the drama and want to see this distilled to 3 lines: https://x.com/nadermx/status/2097414953225310280 https://x.com/nadermx/status/2097414953225310280
  • 6thbit 8d ago
    Any version with a bit more prose for a peasant like me to remotely pretend to grasp it
    • nadermx 7d ago
      [dead]
• dataflow 8d ago
  Is blockchain going to finally be the solution to something? I'm only half joking. Should researchers perhaps put hashes of their attempts on a public blockchain tied to their own public keys, verify their claims asynchronously, and then whoever reveals the first believable attempt gets the credit? I know some people started doing this years ago but now it might need to become standard practice.
• angry_octet 8d ago
  OpenAI cribbing from other researchers. We just have to assume OpenAI is actively adversarial in future. Accidental cyber intrusion is also well within model capability.
• dbuser99 8d ago
  It’s hard to give openai the benefit of doubt here
• kevinbaiv 8d ago
  [flagged]
• harhargange 8d ago
  I have a dumb feeling that the proof will be wrong with serious flaws but that will be found out only after the ipo
• sabujp 8d ago
  created a simulation of the solution to describe what's happening and why it's important for engineers, climate modeling, etc : https://navier-stokes-singularity-simulator.netlify.app/ https://navier-stokes-singularity-simulator.netlify.app/ (updated so that it works better on mobile)
  • HarHarVeryFunny 7d ago
    Is it really important for engineers, etc? In reality you can't have things like infinite velocity, so if Navier-Stokes is predicting blowups, then isn't this a problem with Navier-Stokes not handling some edge cases, not a problem with reality that engineers need to be concerned about?
• itissid 8d ago
  In CS speak very roughly this would mean something like disproving an algorithm by giving it a case that fails it. Right?
• omnium1 8d ago
  [dead]
• fittingopposite 8d ago
  > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . Wow. That sounds like an admission of guilt.
• boardwaalk 8d ago
  I do mean to be critical here. I wish there was better moderation so I could find more conversation about the actual discovery here. There are multiple threads on this and I keep scrolling and only seeing more conversation about the drama. Which is about the least interesting thing IMO. I suppose I’m whistling in the wind here and not helping the situation, but damn.
• onecommentman 8d ago
  When considering such foundational challenges to Mathematical Research and plagiarism as discussed here, we should turn to that elder prophet of our age, Tom Lehrer. Who made me the genius I am today The mathematician that others all quote? Who's the professor that made me that way The greatest that ever got chalk on his coat? [Chorus] One man deserves the credit One man deserves the blame And Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobach— [Interlude] I am never forget the day I first meet the great Lobachevsky In one word he told me secret of success in mathematics: Plagiarize [Verse 1] Plagiarize Let no one else's work evade your eyes Remember why the good Lord made your eyes So don't shade your eyes But plagiarize, plagiarize, plagiarize Only be sure always to call it please, "research" [Chorus] And ever since I meet this man My life is not the same And Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobach— [Interlude] I am never forget the day I am given first original paper to write It was on analytic and algebraic topology Of locally Euclidean metrizations Of infinitely differentiable Riemannian manifolds Боже мой This I know, from nothing What I'm going to do I think of great Lobachevsky and get idea, haha [Verse 2] I have a friend in Minsk Who has a friend in Pinsk Whose friend in Omsk Has friend in Tomsk With friend in Akmolinsk His friend in Alexandrovsk Has friend in Petropavlovsk Whose friend somehow is solving now The problem in Dnepropetrovsk And when his work is done Haha, begins the fun From Dnepropetrovsk to Petropavlovsk By way of Iliysk and over Novorossiysk To Alexandrovsk to Akmolinsk To Tomsk to Omsk To Pinsk to Minsk To me the news will run Yes, to me the news will run [Verse 3] And then I write by morning, night And afternoon, and pretty soon My name in Dnepropetrovsk is cursed When he finds out I published first [Chorus] And who made me a big success And brought me wealth and fame? Nicolai Ivanovich Lobachevsky is his name Oy, Nicolai Ivanovich Lobachev— [Interlude] I am never forget the day my first book is published Every chapter I stole from somewhere else Index I copy from old Vladivostok telephone directory This book was sensational! Pravda—well, Pravda—Pravda said: "Жил-был король когда-то, при нём блоха жила”…it stinks But Izvestia! Izvestia said: "Я иду туда, куда сам царь идёт пешком”…it stinks Metro-Goldwyn-Moskva buys the movie rights for six million rubles Changing title to 'The Eternal Triangle' With Ingrid Bergman playing part of hypotenuse [Chorus] And who deserves the credit? And who deserves the blame? Nicolai Ivanovich Lobachevsky is his name Oy (Tom Lehrer put all of his work in the public domain prior to his passing. Find versions of his performances on YouTube.) https://tomlehrersongs.com/disclaimer/ https://tomlehrersongs.com/disclaimer/
• webcoon 8d ago
  "Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens." At a conservative estimate of GPT 6 Astra pricing, this would have cost upwards of 15 Million dollars for anyone using the OpenAI API! To me this is the one silver lining. Yes, they can solve millennium prize problems, but it still costs a fortune.
  • redwood 7d ago
    The Millenium Prize awards are going to need to be raised!
• lionkor 8d ago
  A couple hundred billion dollars of investment better solve cancer, hunger, and climate change, otherwise they are horribly misplaced :)
• axionbraid 8d ago
  [flagged]
• DeerFreak 8d ago
  Is there a way to know what kind of agentic architecture they used? Or how they prompted/started the problem?
• peter_d_sherman 7d ago
  >"The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. This central region shrinks while it speeds up in such a way that its energy still stays finite, as required by the laws of physics. The technical challenge is for the equations to develop the breakdown through the motion of the fluid itself, rather than, for example, us putting in an infinite force by hand. More mathematically, the terms in the Navier–Stokes equations that describe the motion—acceleration, pressure gradients, momentum transfer, viscosity—must both become big yet cancel in a precise way. This detailed balance leaves a smooth external force even as the velocity of the fluid grows without bound. Diagram of a swirling vortex illustrating inward spiral and axial stretching. A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching." Hmmm, isn't that interesting! (Side note: Apparently we can't "compress" something, but apparently we can move more units of that thing over a specific space in a specific time... hmmm, I wonder what the difference between those two concepts could be...) Main Observation: The image on OpenAI's web page above, looks sort of like the one for the Hopf Fibration: https://en.wikipedia.org/wiki/Hopf_fibration https://en.wikipedia.org/wiki/Hopf_fibration https://www.google.com/search?q=hopf+fibration&udm=2 https://www.google.com/search?q=hopf+fibration&udm=2